Question

Find the \(x\) - and \(y\) -coordinates of the center of mass of the flat triangular plate of height \(H=17.3 \mathrm{~cm}\) and base \(B=10.0 \mathrm{~cm}\) shown in the figure.

Short answer

Answer: The coordinates of the center of mass of the flat triangular plate are (5, 5.77) cm.

Step-by-step solution

Identify the coordinates of the vertices of the triangle

We can consider the base of the triangle to be along the x-axis and one vertex of the triangle at the origin. Then, the vertices of the triangle are A(0, 0), B(10, 0), and C(5, 17.3).

Calculate the x-coordinate of the center of mass

The x-coordinate of the center of mass of a flat triangular plate is given by the average of the x-coordinates of its vertices. So, we can find the x-coordinate of the center of mass using the formula: \(x_{c} = \frac{A_x + B_x + C_x}{3}\) Now substitute the x-coordinates of the vertices A(0), B(10), and C(5) in the above formula: \(x_{c} = \frac{0 + 10 + 5}{3} = \frac{15}{3} = 5 \mathrm{~cm}\)

Calculate the y-coordinate of the center of mass

Similarly, the y-coordinate of the center of mass of a flat triangular plate is given by the average of the y-coordinates of its vertices. So, we can find the y-coordinate of the center of mass using the formula: \(y_{c} = \frac{A_y + B_y + C_y}{3}\) Now substitute the y-coordinates of the vertices A(0), B(0), and C(17.3) in the above formula: \(y_{c} = \frac{0 + 0 + 17.3}{3} = \frac{17.3}{3} = 5.77 \mathrm{~cm}\)

State the coordinates of the center of mass

The coordinates of the center of mass of the flat triangular plate are \((x_c, y_c) = (5, 5.77)\).